STABILITY OF SOLITARY-WAVE SOLUTIONS TO THE HIROTA-SATSUMA EQUATION

被引：0

作者：

Bona, Jerry L. ^{[1
]}

Pilod, Didier ^{[2
]}

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

[2] Univ Fed Rio de Janeiro, Inst Math, UFRJ, BR-21945970 Rio De Janeiro, Brazil

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 27卷 / 04期

关键词：

Solitary waves; stability; nonlinear dispersive wave equations; Korteweg-de Vries-type equations; MODEL-EQUATIONS;

D O I：

10.3934/dcds.2010.27.1391

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The evolution equation u(t) - u(xxt) + u(x) - uu(t) + ux integral(+infinity)(x) u(t)dx' = 0, (1) was developed by Hirota and Satsuma as an approximate model for unidirectional propagation of long-crested water waves. It possesses solitary-wave solutions just as do the related Korteweg-de Vries and Benjamin-Bona-Mahony equations. Using the recently developed theory for the initial-value problem for (1) and an analysis of an associated Liapunov functional, nonlinear stability of these solitary waves is established.

引用

页码：1391 / 1413

页数：23

共 50 条

[41] Invariant Investigation on the System of Hirota-Satsuma Coupled KdV Equation
Hashemi, M. S.
Balmeh, Z.
Akgul, A.
Akgul, E. K.
Baleanu, D.
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017), 2018, 1978
[42] A new method for a generalized Hirota-Satsuma coupled KdV equation
Xie, Manlin
Ding, Xuanhao
APPLIED MATHEMATICS AND COMPUTATION, 2011, 217 (17) : 7117 - 7125
[43] Transformation of a generalized Harry Dym equation into the Hirota-Satsuma system
Sakovich, SY
PHYSICS LETTERS A, 2004, 321 (04) : 252 - 254
[44] Smoothing properties for a Hirota-Satsuma systems
Jimenez, Salvattore
Vera Villagran, Octavio Paulo
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2011, (61)
[45] The decomposition method for a Hirota-Satsuma coupled KdV equation and a coupled MKdV equation
Raslan, KR
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2004, 81 (12) : 1497 - 1505
[46] Approximate Analytic Solutions of Time-Fractional Hirota-Satsuma Coupled KdV Equation and Coupled MKdV Equation
Liu, Jincun
Li, Hong
ABSTRACT AND APPLIED ANALYSIS, 2013,
[47] Multi-component generalizations of the Hirota-Satsuma coupled KdV equation
Chen, Junchao
Chen, Yong
Feng, Bao-Feng
Zhu, Hanmin
APPLIED MATHEMATICS LETTERS, 2014, 37 : 15 - 21
[48] New exact solutions to the generalized coupled Hirota-Satsuma Kdv system
Yong, XL
Zhang, HQ
CHAOS SOLITONS & FRACTALS, 2005, 26 (04) : 1105 - 1110
[49] Novel Exact Solitary Wave Solutions for the Time Fractional Generalized Hirota-Satsuma Coupled KdV Model Through the Generalized Kudryshov Method
Ullah, Mohammad Safi
Harun-Or-Roshid
Ali, M. Zulfikar
Rahman, Zillur
CONTEMPORARY MATHEMATICS, 2019, 1 (01): : 25 - 32
[50] Stability of Solitary-Wave Solutions of Systems of Dispersive Equations
Bona, Jerry L.
Chen, Hongqiu
Karakashian, Ohannes
APPLIED MATHEMATICS AND OPTIMIZATION, 2017, 75 (01): : 27 - 53

← 1 2 3 4 5 →